In a credit contingent contract, payment is dependent on the occurrence of a certain credit event. This class of financial products is broad and provides a natural way for market participants to transfer event risk to dealers. The dealer is exposed to substantial potential losses that can occur with small probability. We are analyzing cancelable interest rate swaps, the most basic structure.
A cancelable swap is like a regular interest rate swap with an uncertain maturity. When a third party defaults the swap terminates without any payment to the counterparty that has the positive mark-to-market on the swap.
Default Independent of Swap Market Value
The bank's client is a French exporter, whose business is mainly concentrated in an emerging market country. The client funds at French franc LIBOR. Based on business analysis, a regular income is expected to be payable in French francs unless the country defaults. In order to hedge the interest rate mismatch between assets and liabilities the client enters into an interest rate swap, that should be canceled if the country defaults. A cancelable swap would be the natural hedge.
In the above example the level of the French franc interest rates and therefore the market value of the swap does not have any impact on the default probability. The theoretical coupon of the swap is set at inception so that the market value of the difference between the fixed and the floating legs discounted at the foreign country's credit curve equals zero. The impact of the credit spread on the equilibrium coupon is shown in figure 2.
Interest Rates Trigger Default
If the foreign country has issued large amounts of French franc-denominated debt to be serviced by floating payments, a substantial increase in the level of the interest rate could trigger default. (This is what happened in the syndicated Eurodollar loan market in Mexico and Brazil, in the early 1980s, when the U.S. interest rates soared). Therefore the probability of cancellation of the swap will be higher when the client has a positive mark-to-market. In order for the client to be compensated for this adverse effect, he would pay a lower fixed coupon than in the zero correlation case. In figure 3 is shown the effect of the correlation between the LIBOR rate and the credit spread. It is important to note that the impact of the correlation will be small if the credit spread exhibits low variability and a high mean reversion level.
Pricing these products can be difficult, but the biggest challenge for the dealer is the risk management. The theoretical price could be a very useful benchmark, but the actual pricing should be done based on the cost of the hedge, including transaction costs and compensation for any residual variance that cannot be hedged.
When the coupon is determined as shown in figure 2 and figure 3, the expected P&L is zero, but it can have high variance, which is driven by the volatility of the swap rate. Therefore for any specific trade it is possible to realize a big gain or loss. The best way to reduce the possibility of extreme losses is to run a well-diversified book (both in terms of market and event risks) of relatively small transactions. Additional hedging could be minimal and the dealer could provide these products to his clients at a very competitive price.
Next we discuss a hedging strategy that, appropriately adjusted, could be implemented in practice. The objective of the hedge is to reduce the variance of the P&L. We assume that there is a market for binary default swaps in the credit of the third party. A binary default swap pays 1 in case of default and 0 otherwise.
It is assumed that the default probability and therefore the default swap premium is independent of the level of the French franc swap rate. The dealer buys or sells an amount of binary default swaps equal to the mark-to-market (positive or negative respectively) of the interest rate swap. In case of default the dealer will lose or gain the mark-to-market on the interest rate swap, but he will realize an offsetting gain or loss on his binary default swap position. The dealer is now exposed to a new risk, which is the cost of the default swaps, which is substantially smaller than the mark-to-market risk he has eliminated. The variance of the P&L has been reduced drastically. The hedge has to be continuously readjusted as interest rates move.
Now we relax the assumption that the default swap premium is known in advance. If the default probability is higher (lower) when the interest rates increase (decrease), the dealer will tend to sell (buy) default swaps when the premium is high (low). Therefore, because of convexity, the hedge will be less (more) costly than in the zero correlation case. The dealer would accept a lower (higher) premium. This is consistent with figure 3.
Markets for Contingent Contracts
Securities whose payoff is contingent on the occurrence of a certain event are more common than one would expect. Due to prepayments, receiving the coupons on a mortgage-backed security is contingent on the interest rate being above a certain level. If homeowners exercise their option rationally, there will be a high degree of correlation between the present value of the mortgage and the probability of contract "cancellation." This leads to substantial convexity in the pricing.
A vulnerable option (the writer of the option can default) is a cancelable option, where the place of the third party is taken by the option writer. Catastrophe and weather bonds are another example where the payoff is contingent on a certain event occurring. In a tender offer situation the bidder would like to enter into a hedging contract (such as a swap, option or forward) that would be activated only if he wins the bid. Modeling of this product is further complicated by moral hazard and adverse selection issues.
This week's Learning Curve was written byAngelo Arvanitis,head of quantitative credit & risk research atParibas.